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G-2021-45

The equilateral small octagon of maximal width

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A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with \(n=2^s\) vertices is not known when \(s \ge 3\). This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximatively 3.24 % larger than the width of the regular octagon: \(\cos(\pi/8)\). In addition, the paper proposes a family of equilateral small \(n\)-gons, for \(n=2^s\) with \(s\ge 4\), whose widths are within \(O(1/n^4)\) of the maximal width.

, 14 pages

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